KR20230081923A - Plate spring structure using negative stiffness phenomenon - Google Patents

Abstract

The present invention relates to a plate spring structure using a negative stiffness phenomenon, and more particularly, to generate a negative stiffness phenomenon by an appropriate arrangement, so that it is useful for an active absorber It relates to a leaf spring structure that can be used.
According to the present invention, by arranging a plurality of plate springs to generate a negative stiffness phenomenon, when used in an active damper, a plate that can be implemented to generate a stress sufficiently smaller than the allowable strength of the plate spring while maintaining low stiffness Provides a spring structure.

Description

Plate spring structure using negative stiffness phenomenon

The present invention relates to a plate spring structure using a negative stiffness phenomenon, and more particularly, to generate a negative stiffness phenomenon by an appropriate arrangement, so that it is useful for an active absorber It relates to a leaf spring structure that can be used.

In order to construct an active damper, it is advantageous to induce low stiffness. Coil springs are mainly used as existing mechanical parts that induce rigidity, but in general, due to structural characteristics, if a low-stiffness coil spring of 10 Hz or less is used to maintain a low natural frequency, the spring cannot overcome the load and is completely compressed. function cannot be maintained or damage occurs. In addition, a long spring is required in order to make low rigidity, so it occupies a large space, and thus it is difficult to satisfy the design result of a practical size.

As a way to overcome this, a leaf spring can be used. However, in the case of using a general leaf spring, in order to perform the function of an effective active damper, it remains a very difficult task to implement to generate a stress that is sufficiently smaller than the allowable strength of the leaf spring while maintaining low stiffness. .

KR 10-1266831 B1

The present invention has been devised to solve this problem, by arranging a plurality of leaf springs to generate a negative stiffness phenomenon, so that when used in an active reducer, the stiffness is sufficiently lower than the allowable strength of the leaf spring while maintaining low stiffness. Its purpose is to provide a leaf spring structure that can be implemented to generate stress.

In order to achieve the above object, a plate spring structure using a negative stiffness phenomenon according to the present invention includes a tuned mass; a support portion coupled to the rim of the leaf spring to support the corresponding leaf spring; a first leaf spring supported by being coupled to the support portion and pre-displaced by at least a portion of the tuning mass; And, a second leaf spring in which the rim portion is coupled to and supported by the support portion at the lower part of the first leaf spring, the rim portion is in contact with the rim portion of the first leaf spring, and predisplacement is applied by at least a part of the tuning mass. Including, a negative stiffness phenomenon is generated in at least one of the first leaf spring and the second leaf spring by the tuning mass.

The leaf spring structure using the negative stiffness phenomenon includes a third leaf spring whose rim portion is coupled to and supported by the support portion under the second leaf spring and pre-displaced by at least a portion of the tuning mass; And, a fourth leaf spring in which a rim portion is coupled to and supported by the support portion under the third leaf spring, the rim portion is in contact with the rim portion of the third leaf spring, and predisplacement is applied by at least a portion of the tuning mass. Further, a negative stiffness phenomenon may be generated in at least one of the third leaf spring and the fourth leaf spring by the tuning mass.

The tuning mass may include the liner.

The leaf spring structure using the negative stiffness phenomenon further includes a liner for maintaining a predetermined distance between the second leaf spring and the third leaf spring and between the second leaf spring and the third leaf spring. can include

According to the present invention, by arranging a plurality of plate springs to generate a negative stiffness phenomenon, when used in an active damper, a plate that can be implemented to generate a stress sufficiently smaller than the allowable strength of the plate spring while maintaining low stiffness This has the effect of providing a spring structure.

1 is a view showing the structure of a passive reducer and an active reducer.
2 is a diagram for comparing performance of a passive reducer and an active reducer.
3 is a diagram showing the structure of a voice coil motor used as an actuator.
4 is a diagram illustrating a simulation model for confirming an effect of an excitation force generated by an actuator on an object to be absorbed.
5 is a diagram illustrating an acceleration response of an absorption target object according to an input of an actuator.
6 is a diagram showing the shape and equivalent stiffness of a plate spring.
7 is a diagram showing mechanical property values of SM45C, a material used for leaf springs.
8 is a diagram showing analysis results according to the number of patterns of leaf springs.
9 is a view showing the results of analysis by reinforcing the stress concentration part with respect to the quadruple structure plate spring in the case of 11 patterns.
10 is a view showing the result of performing the natural vibration analysis of the active damper when the mass is designed to be 2 kg.
11 is a view showing a quadruple plate spring structure.
12 is a view showing the structure of an active damper to which a quadruple plate spring structure is applied.
13 is a diagram for explaining a buckling phenomenon generated in a beam.
14 is a diagram illustrating a quadruple leaf spring structure using a negative stiffness phenomenon.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. Prior to this, the terms or words used in this specification and claims should not be construed as being limited to the usual or dictionary meaning, and the inventor appropriately uses the concept of the term in order to explain his/her invention in the best way. It should be interpreted as a meaning and concept consistent with the technical idea of the present invention based on the principle that it can be defined. Therefore, since the embodiments described in this specification and the configurations shown in the drawings are only one of the most preferred embodiments of the present invention and do not represent all of the technical ideas of the present invention, various alternatives may be used at the time of this application. It should be understood that there may be equivalents and variations.

1 is a view showing the structure of a passive reducer and an active reducer.

A Dynamic Absorber or TMD (Tuned Mass Damper) is a vibration control device that is additionally attached when a structure generates a resonance phenomenon in which the natural frequency and excitation force generated from the outside match. An additional device is attached without changing the existing structure. This is a device that increases the vibration suppression performance of the structure.

The passive reducer of FIG. 1 (a) uses a passive element that does not receive energy from the outside, selects an appropriately sized tuned mass or additional mass (hereinafter referred to as 'tuned mass') m _tuned , and It is implemented by designing and attaching stiffness (K _optimal ) and damping (C _optimal ) considering the characteristics of

The active reducer of FIG. 1 (b) is a vibration suppression device that has better performance and tuning convenience by attaching a sensor and an actuator to the passive reducer and implementing an algorithm through a controller. Instead of stiffness (K _optimal ) and damping (C _optimal ) with optimal parameter values, it has a stiffness K _a of an appropriate size, and the actuator performs a control operation using the signal received from the sensor to determine the mass (M ) and the tuning mass m _tuned of the active damper, more excellent performance can be induced by supplying an appropriate force (f). The illustrated absorption object means various equipment and a base table on which such equipment is placed, and its total mass is M. A vibration isolator composed of a spring (k) and a damper (c) is provided at the bottom.

2 is a diagram for comparing performance of a passive reducer and an active reducer.

Figure 2 (a) is the impulse response for each case where there is no reducer (without TMD), when a passive reducer (Optimal TMD) and an active reducer (Active TMD) are installed, and Figure (b) shows the amplitude ( Bode plots for magnitude and phase are shown. Referring to the drawings, the case of the active absorber exhibits excellent performance in that the shock response disappears faster than the case of the passive absorber and the peak almost disappears in terms of frequency.

3 is a diagram showing the structure of a voice coil motor used as an actuator.

The voice coil motor is a linear actuator that includes a coil and a permanent magnet inside the coil, and can control a driving force by controlling a current flowing through the coil. Since the driving force of these actuators is controlled by changing the control signal supplied from the controller, it is important to select an appropriate stiffness _ka in the design of the active damper.

4 is a diagram illustrating a simulation model for confirming an effect of an excitation force generated by an actuator on an object to be absorbed.

Active dampers result in the problem of determining the tuned mass m _tuned and the stiffness k _a . In general, the larger m _tuned is, the more effective it is, but if it has a large value based on the mass M of the absorber using an active absorber, problems arise in realization, so it is common to determine it at a level of 5 to 10% of M. Therefore, the determination of the stiffness k _a remains an important issue.

4 is a simulation model for confirming the effect of the stiffness k _a and the excitation force generated from the actuator on the mass M of the structure. The structure placed at the bottom is assumed to have 1 degree of freedom, and a mass of 100 kg and a natural frequency of 5 Hz are set. This is because the anti-vibration performance is advantageous with a low natural frequency, so most of the anti-vibration tables use a material of low rigidity that induces a low natural frequency. At this time, the additional mass m _tuned constituting the active absorber is set to 5 kg, and the stiffness K _a is set such that the natural frequency f _na of the TMD becomes 5 Hz, 10 Hz, and 20 Hz. At this time, the low natural frequency is due to the low stiffness. Using this model, the acceleration of the mass M of the object to be absorbed with respect to the input of the actuator can be expressed as a frequency response.

5 is a diagram illustrating an acceleration response of an absorption target object according to an input of an actuator.

If a large acceleration is displayed with respect to the input of the same actuator, the excitation force generated from the actuator has a great influence on the structure, and thus it can be determined as a desirable design result. 5 shows the analysis results of this model. It can be seen that the acceleration of the structure due to the actuation of the actuator shows a larger value as f _na is lower in the band around 5 Hz, which is the natural frequency of the structure of interest. That is, if the stiffness constituting the active damper is high, the effect on the natural frequency of the structure that needs to be controlled is small, so it is difficult to expect good control characteristics. In contrast, the low stiffness of the active absorber shows a large driving force in the actuator of interest around 5 Hz, so good control characteristics can be expected.

6 is a diagram showing the shape and equivalent stiffness of a plate spring, and FIG. 7 is a table showing mechanical property values of SM45C, a material used for the plate spring.

Figure 6 (a) is a view showing a beam supported at both ends and equivalent stiffness thereof by formula, Figure 6 (b) is a view showing the shape of the plate spring used in the present invention viewed from above.

As described above, it is advantageous to induce low stiffness in order to construct an active damper. Coil springs are mainly used as existing mechanical parts that induce rigidity, but in general, due to structural characteristics, if a low-stiffness coil spring of 10 Hz or less is used to maintain a low natural frequency, the spring cannot overcome the load and is completely compressed. function cannot be maintained or damage occurs. In addition, a long spring is required to make low rigidity, so it occupies a large space, and therefore it is difficult to satisfy the design result of a practical size.

Therefore, in order to maintain low rigidity in a small space, a leaf spring 1110 as shown in FIG. 6 below is used. This is a structure in which load points are matched by using several structures that induce appropriate stiffness using both ends support beams, and is designed in a rotational type to save space. Referring to FIG. 6 (a), the equivalent stiffness of a beam supported at both ends is determined by the length (l), the elastic modulus (E) of the material, and the area moment of inertia (I) of the cross section. In addition, the normal stress generated at this time is determined by the bending formula derived based on Hooke's law.

The plate spring 1110 forms a plurality of patterns 100 formed in a groove shape on a plate. The plate spring 1110 performs the function of a spring while generating displacement in the upward and downward directions by the pattern 100 when upward and downward forces are applied.

For the design of the plate spring 1110, the thickness of the plate, the width of the beam, the number of beams, etc. are used as design parameters. The number can be determined by designing one beam and performing pattern copying in the direction of rotation. The applied load is selected as 200 N considering the tuning mass of the active damper, the force of the actuator, and the safety factor, and an appropriate shape design is performed by performing various analyses. It can be seen from the table of FIG. 7 that SM45C, which is the material used, has a Tensile Strength of 490 MPa. That is, a lot of displacement is induced with respect to the applied load, so that the stress generated while maintaining low stiffness is kept below the allowable tensile strength.

8 is a diagram showing analysis results according to the number of patterns of leaf springs.

8(a) is the analysis result of a single plate spring using one plate with a thickness of 4 mm, FIG. 8(b) is the analysis result of a double plate spring using two plates, and FIG. 8(c) shows four This is the analysis result of a quadruple plate spring using plates. In each table, 'Pattern' is the number of patterns, 'Disp.' is the maximum vertical displacement of the leaf spring, and 'Stress' is the stress applied to the leaf spring. In addition, 't' in FIGS. 8(b) and (c) means the thickness of each plate. Each table is a result of performing static analysis while changing the number of patterns.

In the single plate spring of FIG. 8(a), when the pattern is 8, a displacement of 12.8 mm occurs, and the stress at that time has a value much larger than the allowable strength.

In the double plate spring of FIG. 8(b), the parallel support structure causes the stiffness of each spring to be added, so to make the same stiffness as the case of a single leaf spring, if two leaf springs having half the stiffness are used do.

The analysis results are shown in the table of FIG. 8(b). When the thickness is 1.5 mm and the pattern is 5, the displacement is 25.6 mm, so it has very low stiffness, but the stress greatly exceeds the allowable stress, so it cannot be used. However, when the thickness is 2.0mm and the pattern is 8, it has a displacement of 16.0mm, but the stress is smaller than that of a single plate spring with a displacement of 12.8mm.

In other words, it can be confirmed that structural design with larger displacement and lower stress is possible by adjusting the pattern and thickness. In addition, the parallel leaf spring of the double structure is advantageous in terms of the displacement-to-stress ratio. Therefore, better results can be expected if the leaf spring is expanded in quadruple.

Figure 8 (c) shows the results of arranging the plate spring in a quadruple parallel structure and analyzing the displacement and stress according to the change of various patterns. In the table of FIG. 8(c), the thickness of each plate is fixed at 1.5 mm and only the number of patterns is changed.

As the number of patterns increases, the displacement proportionally increases, but the stress is not proportional. It can be seen that the stress is the smallest when the pattern is 10, but the displacement increases very greatly compared to single or double. Compared to the stress of 709 MPa at 16.0 mm displacement of the double structure, pattern 10 of the quadruple structure increased the displacement to 19.3 mm, but the stress significantly decreased to 554 MPa.

Since the voice coil motor of the actuator used in this design has a stroke of +/- 15 mm, when the pattern is 11 in a quadruple structure, the displacement of 21.2 mm is not implemented. Therefore, even if it is adopted, the stress generated is estimated to be below the allowable strength, so it was selected, and the process of confirming the stress using finite element analysis was repeated while reinforcing the local stress generating area.

9 is a view showing the results of analysis by reinforcing the stress concentration part with respect to the quadruple structure plate spring in the case of 11 patterns.

The result of the analysis was shown by reinforcing the part where the stress is concentrated in the quadruple structure of the plate spring with the thickness of 1.5 mm and the number of patterns of 11. It can be seen that the displacement is 21.2 mm for a load of 200 N, and the stress at that time is reduced to 335 MPa. Also, as mentioned earlier, the voice coil motor of the actuator has a stroke of +/-15 mm, so the actual stress generated decreases proportionally and can be estimated to be 237 MPa, which is about half of the allowable strength, with a safety factor of 200 It can be confirmed that the design has no problem in operation with %.

10 is a view showing the result of performing the natural vibration analysis of the active damper when the mass is designed to be 2 kg.

It can be seen that the natural frequency of mode 1 in FIG. 10 (a) shows a mode shape in the vertical direction and has a natural frequency of 10.4 Hz.

FIG. 11 is a view showing a quadruple leaf spring structure 1100, and FIG. 12 is a view showing the overall structure of an active reducer 1000 to which the quadruple leaf spring structure 1100 is applied.

The support part 1130 is fastened to the mass M of the vibration control object, and the middle part supported by the plate spring 1110 uses several liners 1120 to adjust the interval between the plate springs 1110. there is. This part corresponds to the tuning mass part of the active damper 1000 to which the driving force of the actuator 1200 is applied. Even when the actuator is not driven, all four leaf springs 1110 deflect downward due to a static load due to gravity.

FIG. 12(a) is a perspective view of a cross section of the active reducer 1000, and FIG. 12(b) is a perspective view of the shape of the active reducer.

12, the tuned mass m _tuned is the sum of the mass of the liner 1120 and the mass of the permanent magnet 1220 of the voice coil motor 1200 as an actuator. On the other hand, the coil unit 1210 of the voice coil motor is fixed to the lower end and is fixed to the suction object M, which is a target of vibration control.

In the active damper 1000 adopting the quadruple plate spring structure 1100 of FIG. 11, it was confirmed that the natural frequency was 10.9 Hz in the initial state, and the dynamic stiffness ka was 9380.9 N/m.

Hereinafter, a principle applied to reduce the rigidity of the quadruple leaf spring structure 1100 will be described with reference to FIG. 13, and the quadruple leaf spring structure 1100 of the present invention applying such a principle will be described with reference to FIG. Let's explain.

13 is a diagram for explaining a buckling phenomenon generated in a beam.

Negative stiffness means that the value of stiffness becomes negative at F=kx, which represents the relationship between stiffness (k), external force (F), and displacement (x) of a spring, and is considered a structure that cannot be physically possessed in general mechanical structures. However, as shown in FIG. 13, a method of implementing using a buckling phenomenon generated in a beam having a long slenderness ratio has been studied.

(1) of FIG. 13 (a) is the initial state of a beam with both ends fixed vertically, and a preload is already applied to start in a buckling state. At this time, it is obvious that when the force F _t applied in the horizontal direction to the center is small, it has positive stiffness for a minute size. This corresponds to section (1) in the graph of FIG. 13(b). The stiffness determined by the displacement of the horizontal axis and the force of the vertical axis becomes the slope, which has a positive sign.

However, when a continuous load is applied and the transition is made to the state of (2) in FIG. 13 (a), the state of buckling is automatically moved from the state of (3) in FIG. 13 (a). That is, in the transition period, even if the small external force F _t becomes negative, it moves to state (3), so it shows the effect of showing a phenomenon of negative stiffness. This shows the interval (2) in the graph of FIG. 13(b), and the slope has a negative sign. Therefore, the displacement section showing this transition characteristic is a structure with negative stiffness.

14 is a diagram illustrating a quadruple leaf spring structure 1100 using a negative stiffness phenomenon.

In the initial state of FIG. 14 (a), when each leaf spring 1110 is supported in a contacting manner at the support part 1130, a preload is naturally applied by the liner 1120, and it behaves in the same shape as in FIG. 14 (b) will do At this time, the expression 'contacting' is not necessarily limited to that each leaf spring 1110 'meeting' at the support part 1130 as shown in FIG.

That is, the part where the plate spring 1 (1111) is coupled to the support part 1130 and the part where the plate spring 2 (1112) is coupled to the support part 1130 are in contact with each other at the support part 1130 as shown in FIG. , A state in which the part where the plate spring 3 (1113) is coupled to the support part 1130 and the part where the plate spring 4 (1114) is coupled to the support part 1130 are in contact with each other at the support part 1130 as shown in FIG. 14 (a) is formed with

When the structure of FIG. 14 (a) is deformed by receiving a load from a mass body, it behaves in the shape shown in FIG. 14 (b). At this time, the liner 1120 constitutes a part of the tuning mass that causes the pre-displacement, and the permanent magnet 1220 of the actuator 1200 as described above with reference to FIG. 12 also constitutes a part of the tuning mass. That is, from the upper end, leaf spring 1 (1111) and leaf spring 3 (1113) are placed in the transition section in the negative stiffness structure as described with reference to FIG. 13, so that negative stiffness is induced. However, leaf spring 2 (1112) and leaf spring 4 (1114) perform a behavior with a general positive stiffness, and the stiffness of the entire system is the sum of the stiffness of the individual leaf springs (1111, 1112, 1113, 1114). , it cannot always be regarded as negative stiffness. However, lower rigidity is induced compared to the installation structure of a general quadruple leaf spring. In addition, the size of the preload is easily adjusted according to the thickness of the liner 1120 inserted between the plate springs, so that it has a structure that can be adjusted to an appropriately low stiffness.

Here, when the load is further applied and the leaf spring 1 (1111) and the leaf spring 3 (1113) cross the transition section, positive stiffness is induced again, so the size of the stiffness is the same as the installation structure of a general quadruple leaf spring. have Therefore, in order to maintain low stiffness, it is set to operate only within the transition period.

The quadruple plate spring structure 1100 using the negative stiffness phenomenon formed in this way was measured to have a natural frequency of 7.9 Hz in the static deflection state of FIG. 14(b), and also When the dynamic stiffness of the active reducer 1000 to which the plate spring structure 1100 is applied is extracted in consideration of the tuned mass m _tuned , it is confirmed that ka is 4927.7 N/m, which is 44.5% higher than the active reducer of FIG. It can be seen that the stiffness is reduced. From this, it can be confirmed that when the quadruple leaf spring structure 1100 using the negative stiffness phenomenon of FIG. 14 is mounted on the active absorber 1000, it has a very effective effect.

1000: active reducer
1100: plate spring structure
1110: leaf spring
1111: leaf spring 1
1112: leaf spring 2
1113: leaf spring 3
1114: leaf spring 4
1120: liner
1130: support
1200: actuator
1210: voice coil
1220: permanent magnet

Claims (4)

As a plate spring structure using the negative stiffness phenomenon,
tuning mass;
a support portion coupled to the rim of the leaf spring to support the corresponding leaf spring;
a first leaf spring supported by being coupled to the support portion and pre-displaced by at least a portion of the tuning mass; and,
A second leaf spring in which a rim portion is coupled to and supported by the support portion under the first leaf spring, the rim portion is in contact with the rim portion of the first leaf spring, and a pre-displacement is applied by at least a part of the tuning mass.
Including, wherein a negative stiffness phenomenon is generated in at least one of the first leaf spring or the second leaf spring by the tuning mass,
Plate spring structure using a negative stiffness phenomenon comprising a. The method of claim 1,
a third leaf spring supported by being coupled to the support portion under the second leaf spring and pre-displaced by at least a portion of the tuning mass; and,
A fourth leaf spring in which a rim portion is coupled to and supported by the support portion under the third leaf spring, the rim portion is in contact with the rim portion of the third leaf spring, and a pre-displacement is applied by at least a part of the tuning mass.
Including more,
A negative stiffness phenomenon is generated in at least one of the third leaf spring and the fourth leaf spring by the tuning mass.
A leaf spring structure using a negative stiffness phenomenon, characterized in that. The method of claim 2,
The tuning mass is,
containing the liner
A leaf spring structure using a negative stiffness phenomenon, characterized in that. The method of claim 2,
A liner maintaining a predetermined gap between the second leaf spring and the third leaf spring and between the second leaf spring and the third leaf spring
A leaf spring structure using a negative stiffness phenomenon, characterized in that it further comprises.

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